-----Original Message-----
>From: marker-fJPbM2L9mBP2fBVCVOL8/A@xxxxxxxxxxxxxxxx
>To
say a bit more about your original question.
>Tom Scanlon (building on
work of Pop, Poonen and others) has
>recently proved that if K is a
finitely generated field, there is a
>sentence describing K up to
isomorphism among the finitely generated
>fields. In particular, this
proves Pop's conjecture that elementarily
>equivalent finitely generated
fields are isomorphic.
That's great, just the result I need.
Can there be two nonisomorphic
countable fields which have the same
finitely generated subfields? (This
question is slightly imprecise,
because an easy way out would be if they
have the same isomorphism
classes of finitely generated subfields but
different numbers of some
given isomorphism class, if there is such an easy
way out modify my
question in the obvious way).
Is the answer
different for char 0 and positive characteristic? (In positive characteristic I
can see non-separability creating difficulties....)
--
JS
